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Linear and nonlinear geometric optics. Part 2. The Vlasov-Maxwell equations

Published online by Cambridge University Press:  13 March 2009

Jonas Larsson
Jonas Larsson
Affiliation:
Department of Plasma Physics, Umeå University, S-90187 Umeå, Sweden
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Abstract

Local tensors determining the geometric-optics description of a Vlasov-Maxwell plasma are considered. The linear and quadratic current responses on a small-amplitude electromagnetic perturbation are given by expressions for the local admittance tensors. These explicitly exhibit symmetries that imply the linear conservation of wave action, if wave-particle interactions are neglected, and the corresponding quadratic conservation laws. Considering, for example, the resonant interaction between three geometric-optics modes the Manley—Rowe relations accordingly follow. Various extensions of the results, including consideration of higher orders in the small amplitude, strong space and time dependence of the background plasma, relativistic theory and the gyrokinetic approximation as well as some corresponding results for important fluid models, may be obtained straightforwardly either directly or by combining the results of this paper with those of previous work.

Type
Research Article
Information
Journal of Plasma Physics , Volume 42 , Issue 3 , December 1989 , pp. 495 - 506
Copyright
Copyright © Cambridge University Press 1989

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References

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